Fuel 206 (2017) 675–683

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Full Length Article

One way of representing the size and shape of biomass particlesin combustion modeling

http://dx.doi.org/10.1016/j.fuel.2017.06.0520016-2361/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: anna.trubetskaya@ltu.se (A. Trubetskaya).

Anna Trubetskaya a,⇑, Gert Beckmann b, Johan Wadenbäck c, Jens Kai Holmd, Sitaram P. Velaga e,Roman Weber f

aDivision of Energy Science, Luleå University of Technology, 97187 Luleå, SwedenbRetsch GmbH, Retsch Allee 15, 42781 Haan, GermanycAmager Power Plant, HOFOR A/S, Kraftværkvej 37, 2300 Copenhagen S, DenmarkdDONG Energy Thermal Power A/S, Nesa Alle 1, 2820 Gentofte, DenmarkeDepartment of Health Sciences, Luleå University of Technology, 97187 Luleå, Swedenf Institute of Energy Processes Engineering and Fuel Technology, Clausthal University of Technology, 38678 Clausthal-Zellerfeld, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 22 March 2017Received in revised form 8 June 2017Accepted 12 June 2017

Keywords:Biomass2D dynamic imagingFBRMLaser diffractionSieving

This study aims to provide a geometrical description of biomass particles that can be used in combustionmodels. The particle size of wood and herbaceous biomass was compared using light microscope, 2Ddynamic imaging, laser diffraction, sieve analysis and focused beam reflectance measurement. The resultsfrom light microscope and 2D dynamic imaging analysis were compared and it showed that the data onparticle width, measured by these two techniques, were identical. Indeed, 2D dynamic imaging wasfound to be the most convenient particle characterization method, providing information on both theshape and the external surface area. Importantly, a way to quantify all three dimensions of biomass par-ticles has been established. It was recommended to represent a biomass particle in combustion models asan infinite cylinder with the volume-to-surface ratio (V/A) measured using 2D dynamic imaging.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Biomass firing is used for power generation and is consideredan important step in the reduction of greenhouse gas emissions.Anthropogenic CO2 emissions can be decreased by biomass co-firing due to the lower regeneration time of biomass comparedto bituminous coal. Thus, CO2 released with biofuels can be recon-sumed faster by plants via photosynthesis than the time needed toregenerate coal. The milling process is a necessary step in suspen-sion firing [1]. Size reduction improves fuel conversion processesbecause of the creation of larger reactive surface areas [2,3]. Bio-mass is, due to its fibrous structure, difficult to mill. Since the heat-ing value of biomass is lower than coal, more biomass has to beused in order to achieve the same power output [4,5]. Increasedenergy input into biomass comminution affects the total efficiencyof a power plant, and too large particles often cause problems withflame stability and burnout. Fuel characterization plays an impor-tant role in combustion modeling [6–11]. The surface area and vol-ume of the particle are important parameters since they determinecombustion rates and define residence time. Various biomass

shapes result in different volume-to-surface area ratios, whichare important parameters in describing heat and mass transferprocesses. For a given volume, spheres represent the largestvolume-to-surface area ratio of any shape, which makes anassumption of spherical particles in combustion modeling ratherconservative. Particle size analysis methods that assume a constant(spherical) shape are inadequate for biomass characterization sinceirregularly shaped particles are most often present. Furthermore, adisagreement between particle size distributions obtained bymany particle size measurement techniques has been observed[12]. Most particle analyzers use one geometrical parameter byassuming a spherical form. However, as the fuel particle shapebecomes more complex, at least two parameters (width andlength) are necessary to describe the particle size. Despite numer-ous studies on biomass particles [7,13,14,9–11], there is no consen-sus on how to represent a biomass particle in combustion models.The common way involves approximating of the particle shape toregular geometrical bodies (e.g. parallelepiped, cylinder, cubes,ellipsoids). In combustion models from Yang et al. [14] and Yinet al. [13], particles are represented by cylindrical and sphericalshapes, whereas Thunman et al. [7] treat particles in a one-dimensional model as plates, cylinders, and spheres. The accuracyof particle models depends on both correct size distribution and

Nomenclature

A particle surface area [m2]AR aspect ratiob particle width [m]cp specific heat capacity [J (kg K)�1]d diameter [m]f dimensionality factorl particle length [m]L chord length [m]m number of size classesn number of counts per size classMi class midpoint [m]N class numberP perimeter of a particle projection [m]r particle radius [m]r1; r2 distances from the area center to the particle edges [m]q3 histogramq3 frequency particle distribution, based on volume [% mm�1]

Q3 cumulative particle distribution, based on volume [%]SPHT circularity (sphericity)Symm symmetryt time [s]T temperature [�C]V volume [m3]w size class weightxcmin smallest maximal chord [m]xMamin Martin minimum diameter [m]xFemax Feret maximum diameter [m]q density [kg m�3]k thermal conductivity [W (m K)�1]e effectivep particles solid phasetotal total

676 A. Trubetskaya et al. / Fuel 206 (2017) 675–683

characterization of fuel inhomogeneity in terms of shape andstructure. The objective of this study is twofold: (1) to provide ageometrical description of biomass particles that can be used incombustion model; (2) to make suggestions for the size and shapeof biomass particles. In this work, the biomass particles’ size andshape are characterized by using both 2D dynamic imaging analy-sis and microscopy. 2D dynamic imaging results are comparedwith particle size data obtained using focused beam reflectancemeasurement, laser diffraction, and sieving techniques.

2. Materials and methods

2.1. Raw material characterization

Table 1 lists samples which were used in the particle size andshape characterization study. Wheat straw and wood pellets repre-sent the fuel types which are commonly used for suspension firedcombustion with 100% biomass. It is a challenge to obtain highoperational flexibility at power plants by application of a broadbiofuel range. Therefore, poplar, which is among the fastest grow-ing trees in the world, was selected for this study [15]. The mois-ture content and bulk density were measured using standardmethods described in EN ISO 18134-1:2015 and EN ISO17828:2015. The ash content was determined using a standardash test at 550�C, according to the procedure described in EN ISO18122:2015. The 8 mm pellets, without additives or bindingagents, were produced in Latvia (LatGran). The pellets were trans-ported to Avedøre power plant and comminuted in the horizontalLoesche roller mill. Pulverized wood was sampled from the pipe-line (running to the burners) through a side opening by using arotorprobe. Pellets consisted of 10% hardwood and 90% softwood,and were produced from 70% fine sawdust and 30% coarse

Table 1Samples specification. The bulk density, ash (% dry basis) and moisture (% as rewood pellets. Samples were comminuted in the rotor- and Loesche roller millsrotorprobe and a micro-riffler.

IdentifierPoplar

Mill type Rotor millSampling method Micro-rifflerBulk density, g cm�3 1.4Ash, % dry basis 1.3Moisture, % as received 7.9

sawdust. A larger percentage of softwood contains Scots pine(Pinus sylvestris), Norway spruce (Picea abies) and European aspen(Populus tremula), whereas a smaller percentage of hardwood con-sists of birch (Betula spp) and alder (Alnus spp), according to thefeedstock classification described in EN ISO 17225-1. The age ofthe roundwood with bark used for making pellets ranged from15 to 95 years. Poplar and wheat straw samples were milled in aZM200 rotor mill (Retsch GmbH, Germany) whereas pellets werecomminuted in a LM 23.2 D horizontal roller mill (Loesche GmbH,Germany). All samples were milled to 0.5 mm. Biomass sampleswere sieved to the 0.71–1 mm particle size fraction. Under fastheating conditions, which are relevant to suspension firing, bio-mass particles with mean diameters < 0.425 mm may be consid-ered as thermally thin based on the previous modeling results[16], while the intra-particle heat conduction in larger particlesplays a key role in biomass devolatilization. The previous resultsalso indicated that the larger wood particles (0.85–1 mm) requiredmore than 1 s in the wire-mesh and drop tube reactors at 1000�Cfor complete conversion [17]. Therefore, the large biomass parti-cles were selected for the shape characterization study becauseparticles of size > 0.7 mm can often cause problems with flamestability and burnout. Prior to the analysis, biomass samples weredivided into equal (100 mg) fractions using a PT100 micro-riffler(Retsch GmbH, Germany).

2.2. Particle size and shape characterization

2D dynamic imaging analysis. The particle size and shape weremeasured using the CAMSIZER (Retsch GmbH, Germany), designedfor the particle size range from 0.03 to 30 mm. Particle shadows(projected area) were captured by two cameras: a zoom–camera,designed for the analysis of smaller particles, and a basic–camera

ceived) content were determined for poplar, wheat straw and pulverized. Prior to particle size and shape analysis, samples were collected using a

SamplesPulverized wood pellets Wheat straw

Loesche roller mill Rotor millRotorprobe Micro-riffler1.3 1.40.5 4.17.8 10

Fig. 1. Martin minimal (xMamin), smallest maximal chord (xc min) and Feret maximal(xFemax) diameters for a particle projection, as also shown in the Supplementarymaterial.

Fig. 2. Definition of symmetry.

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that was able to detect larger particles. The particle projected areawas determined using the CAMSIZER 6.3.10 software (RetschGmbH, Germany) which evaluates the particle size from the cap-tured images by calculating the three parameters shown inFig. 1. The smallest maximal chord (xc min) is defined as the smallestof all maximum chords of a particle projection. The Martin diame-ter is a characteristic length that divides the projected particle areainto two equal halves [18]. The minimal Martin diameter (xMamin) isdetermined from the smallest Martin diameter of a particle projec-tion [19]. The Feret diameter is a distance between two tangentsplaced perpendicular to the measurement direction [18]. The Feretmaximal diameter is the longest Feret diameter of all measuredFeret diameters of a particle projection [19]. The particle size dis-tribution, based on the volume, as shown in the Supplementarymaterial, is represented by the xMamin diameter. For the particle sizeanalysis, a 100 mg sample was used.

Shape characterization. In the present study, particle shape ischaracterized by both the sphericity (SPHT) and the aspect ratio(AR). Sphericity is one of the most commonly used parameters toexpress the deviation of a two-dimensional particle image from asphere / circle and is defined as

SPHT ¼ 4 � p � AP2 ; ð1Þ

where P and A are the measured perimeter and area of a particleprojection, respectively. A particle is considered to be sphericalwhen sphericity is equal to 1, and non-spherical when it is lessthan 1. The aspect ratio is defined as the ratio of particle width(b = xMamin) to the particle length (l = xFemax) so that

AR ¼ bl: ð2Þ

Particle symmetry (Symm) is defined as

Symm ¼ 12

1þ minr1r2

� �� �; ð3Þ

where r1 and r2 are distances from the area center to the particleedges on the same line. The center (C) of area in Fig. 2 is determinedby the CAMSIZER software. Many lines are drawn so that each onepasses through the area center between the particle’s edges. Thesymmetry is calculated from the smallest ratio of the resulting seg-ments (r1 and r2). For highly symmetrical particles like circles,ellipses or squares, the symmetry nears one. The center point

divides each line in two parts. For asymmetrical particles (e.g. bro-ken beads, triangles), the symmetry is less than one. The symmetryvaries from 0 to 0.5, and r1 and r2 overlap, if the center of the area isoutside of a particle so that

r1r2

< 0: ð4Þ

The symmetry is equal to 0.5, if the center of the area is exactly atthe particle border.

Sieving. A vibrating AS 200 sieve shaker (Retsch GmbH, Ger-many) comprising seven sieves ranging from 0.25 to 4 mm inopening size and a bottom pan (< 0.25 mm) was used. The sievinganalysis is described in EN ISO 17827-2:2016. Particles remainingon each sieve and in a bottom pan were collected and weighedusing an electronic top pan balance (± 0.01 g accuracy). The cumu-lative retained undersize is the mass passed from the previoussieve, minus the mass retained on the current sieve [20]. Sievingwas conducted for 15 min at 3 mm amplitude [21].

Particle size distribution. The results are presented as a cumula-tive particle size distribution, based on volume (Q3). The cumula-tive particle size distribution is described in EN ISO 9276-1:1998,and is defined as

Q3ðxMamin;mÞ ¼Xmi¼1

q3ðxMamin;iÞDxMamin;i; ð5Þ

where q3 is the area of the histogram. The results of a particle sizeanalysis are also presented as a frequency distribution over xMamin,based on volume (q3), so that

q3ðxMaminÞ ¼ dQ3ðxMaminÞdxMamin

: ð6Þ

The characteristic diameters, obtained from sieving and 2Ddynamic imaging, were defined based on three sizes within theentire population: d10, d50, d90. The d50 value is the median par-ticle size within the population, with 50% of the population greaterthan this size, and 50% smaller than this size. Similarly, 10% of thepopulation is smaller than the d10 size; while 90% of the popula-tion is smaller than the d90 size [22]. All measurements were con-ducted in triplicate to establish repeatability which exceeded 95%confidence intervals, as shown in the Supplementary material.The measurement inaccuracy from sieving analysis was mainlycaused by weighing errors.

Light microscopy. Light microscopy of sawdust and disintegratedpellets was conducted using a 1750 microscope heating stage(Leica Microsystems, Germany) in order to characterize the particleshape. Digital images were captured using a camera attached tothe microscope and then analyzed using the software that incorpo-rates a simple ruler. The particle geometric parameters were mea-sured manually using appropriate diameter definitions. At least440 particles are required to obtain 10 particles in each fractionfor statistically reliable results. In the microscopy analysis, about500 biomass particles were characterized. The width and lengthof a biomass particle were analyzed using a ruler in the micro-scope’s software. Smaller particles were analyzed on a piece of

(a): Biomass particle (b): Width and length (c): Thickness

Fig. 3. Measurement of particle three dimensions (width, length, thickness) by the light microscopy.

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adhesive tape. A single biomass particle was manually rotated by90� in the sample plane to determine all three dimensions (SeeFig. 3).

Laser diffraction. The particle size distribution of biomass sam-ples was determined by a 2000 particle size analyzer (MalvernInstruments Ltd, UK) using a wet method. The biomass sampleswere dispersed in ethanol. All measurements were made at roomtemperature and at 3200 rpm on at least two samples. The refrac-tive indices of biomass and ethanol were taken as 1.53 and 1.33,respectively [23]. The Sauter mean diameter was calculated asthe surface area moment mean, and defined as

D32 ¼P

nid3i

nid2i

: ð7Þ

The volume mean diameter (D43) was calculated as follows

D43 ¼P

nid4i

nid3i

; ð8Þ

where ni is the number of particles with measured diameter di.Focused beam reflectance measurement. The particle size distri-

bution was determined using a G400 focused beam reflectanceanalyzer (Mettler Toledo, UK). The focused beam of laser lightscans across individual particles at a fixed scan speed [24]. Thebackscattered light is detected as a signal issued from one particleedge to an opposing edge. The pulse signal duration is multipliedby the scan speed to calculate the chord length. A 1 g of biomasswas added to a 200 ml glass beaker filled with methanol. The bio-mass particles were stirred using an anchor type stirrer at 200 rpmat room temperature. Five measurements, each of 15 min duration,were made on each sample, and the data was recorded using theFBRM acquisition software. The chord lengths, in the range of 1to 1000 lm, were split into ninety classes (N = 90). The total num-ber of counts per class (ni) is determined as

ntotal ¼XN1

ni: ð9Þ

The results of a particle size analysis by FBRM are always pre-sented as an unweighted chord length distribution. For any particleshape, the number of small chord length counts statistically out-weighs the large particle chord length counts [25]. The classweighting was used in order to emphasize the longer chords,which represent the most likely lengths of wood fibers. A class-specific weight (wi) to the number of counts (ni) is then used tocalculate weighted chord length so that

Li ¼ wi � ni: ð10ÞThe weights (wi) are obtained from the class midpoint (Mi)

wi ¼ MjiXN

i¼1Mj

i

� N: ð11Þ

In Eq. 11, j = 0 and j = 2 are unweighted and square-weightedparticle size distributions, respectively. The raw chord length data(j = 0) is first collected by the FBRM probe, and then weighted usingthe square-weighting function. The mean chord length on asquare-weighted basis is calculated as

L ¼XN

i¼1niM

3iXN

i¼1niM

2i

: ð12Þ

Similar to volume-weighted distributions, the square-weighteddistributions are sensitive to the amount of large particles. Thesquare-weighted mean chord length is equivalent to the Sautermean diameter [26–28]. The results of a particle size analysis arepresented as a square-weighted frequency distribution and calcu-lated as

q3ðLÞ ¼niL

2iXN

i¼1ðniL

2i Þ: ð13Þ

The FBRM results of Heath et al. [27] showed that the square-weighting is effectively a cube (volume) weighting and is compara-ble to the volume-based distribution used in laser diffraction.

3. Results

3.1. Particle size analysis

Because of the coupling between chemistry and heat and masstransfer during particle conversion, fuel particle size has a notice-able effect on combustion process characteristics. Thus, the choiceof the suitable particle size descriptors is relevant. In 2D dynamicimaging, the minimal Martin diameter (xMamin) represents a parti-cle width, which is larger than its thickness. The Feret maximaldiameter, representing the length, is greater than the width. There-fore, the Martin minimal (xMamin) and Feret maximal (xFemax) diam-eters are suitable parameters to represent the width and length ofbiomass particles, confirming previous results of Trubetskaya et al.[29]. The most suitable descriptor of particle size, when character-ized using sieving and 2D dynamic imaging, is the smallestmaximal chord (xc min) [19]. The difference between particle sizedistributions over xMamin and xc min diameters is small, as shownin Supplementary Fig. S-5. Thus, the particle width can be repre-sented by xc min diameter when the 2D dynamic imaging device isnot available. Fig. 4 shows particle size distributions for poplar,pulverized wood sample and wheat straw, characterized using

Fig. 4. Cumulative particle size distribution Q3, based on volume, for poplar,pulverized wood and wheat straw samples characterized by the sieving, 2Ddynamic imaging (xMa;min), laser diffraction and focused beam reflectance technique.

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the sieving, 2D dynamic imaging, laser diffraction and focusedbeam reflectance technique. The data obtained by different particlesize characterization techniques is repeatable, as shown in the

Supplementary material. The particle size analysis indicated thatpulverized wood contained a larger fraction of small particles com-pared to poplar and wheat straw. The poplar particle size distribu-tion was more heterogeneous than those of other fuels. Fig. 4shows that sieving and 2D dynamic imaging produced very similarsize distributions for all biomass samples, while a significant devi-ation was observed when compared with the results from the laserdiffraction and the FBRM. The 2D dynamic imaging captures theshadows of randomly orientated 3D particles. 2D projections of a3D particle and their dependency on the orientation and shapecan be recorded by CAMSIZER cameras in various ways. Gil et al.[30] reported that sieve size corresponds to biomass particle width(shorter dimension) with sieving efficiency around 70% dependingon the feedstock and considered size fraction. The square-shapedsieve apertures allow the passage of about 0.8 times the width ofthe particle [31]. During sieving, particles always fall through thesieves with their smallest two-dimensional projection, which doesnot appear the case for biomass particles. In 2D dynamic imagingof elongated biomass particles, the width of a particle projectiondoes not change significantly, while the length of a particle isstrongly influenced by the particle rotation / orientation in themeasurement shaft. The xMamin diameter does not change as exten-sively as the xc min diameter. The sieving curve was close to the 2Ddynamic imaging curve representing xMamin particle model for allsamples. Overall, sieving is more convenient when a large biomasssample quantity has to be analyzed and when the particle sizeexceeds the measurement limitations of other sizing techniques,while 2D dynamic imaging is recommended when informationabout particle shape is required. Particle size distributions mea-sured by 2D dynamic imaging deviate significantly from thoseobtained using the FBRM device. 2D dynamic imaging evaluatesthe particle size based on attributes of non-spherical shapes. TheFBRM device measures chord lengths, where a chord length isdefined as a straight line between any two points on the edge ofa particle. The accuracy of particle size characterization using theFBRM device might be influenced by the various shapes of a bio-mass particle with broken edges. The results of the laser diffractionanalysis showed that both poplar and wheat straw samples con-tained a larger fraction of course particles - a result which wasnot in agreement with other size characterization techniques.The difference between the particle size distributions measuredby the laser diffraction and the other techniques is large. Since bio-mass particle shapes deviate significantly from a sphere, the spher-ical assumptions in the optical models are not valid. Thus, the laserdiffraction analysis does not characterize the real size of biomassparticles. The discrepancy was partly due to the fact that the laserdiffraction measures the diameters of equivalent volume particlesfrom the diffraction signals [32–35]. The wrong assumption of ran-dom orientation of fibers in the laser diffraction affects measure-ment accuracy [32,36].

3.2. Particle shape analysis

The particle shape was characterized using both the 2Ddynamic imaging instrument and light microscopy. The small bio-mass particles of size <0.5 mm were more elongated (SPHT = 0.31and aspect ratio AR = 0.11), as shown in Fig. 5. The aspect ratio ofbiomass particles measured by 2D dynamic imaging over xMamin

decreased from 0.25 to 0.11 with decreasing particle size, indicat-ing that larger particles exhibited a more elongated shape. Thesphericity (mean SPHT of all samples = 0.51) and the aspect ratio(mean AR of all samples = 0.32) for particle fractions >0.5 mmindicate that they were more square-shaped. Symmetries of poplarand wheat straw particles were similar; particles were polygonaland symmetrical with holes (Symm = 0.8). Compared to the poplarand wheat straw samples, the pulverized wood showed a stronger

Fig. 5. Shape factors (sphericity/circularity and symmetry) in comparison to the aspect ratio (b/l) of poplar, pulverized wood and wheat straw samples which were sieved tothe 0.71–1 mm fraction, and characterized by 2D dynamic imaging.

680 A. Trubetskaya et al. / Fuel 206 (2017) 675–683

anisotropy in shape (Symm = 0.68), which might be caused by theparticle edge deformation during secondary comminution. Overall,2D dynamic imaging analysis showed that the particles of adifferent size had similar rectangular shapes and that the ratiobetween particle dimensions did not change significantly withdecreasing particle size, which is in line with the results of Cardosoet al. [37]. In Fig. 6, the light microscopy results showed that wheat

straw particles are elongated. The main difference among the fuelswas that the pulverized wood formed more square-shaped parti-cles while the particles of poplar and wheat straw were elongated,confirming the results of 2D dynamic imaging in Fig. 5. There waslittle change in the average particle shape among the size classes.The major drawback of the 2D dynamic imaging is that two-dimensional projections can be generated only. Consequently, the

Fig. 6. Light microscopy images of (a) poplar, (b) pulverized wood, and (c) wheatstraw particles.

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third dimension cannot be obtained, and for the particle volumecalculation, the thickness is often assumed to be equal to thewidth. In order to examine the accuracy of this simplification,the biomass particles were analyzed using 2D dynamic imagingand light microscopy. In terms of absolute accuracy, the micro-scopy provides a high resolution and high magnification images,but they only represent a small sample amount. The 2D dynamicimaging results, together with the light microscopy data, areshown in Supplementary Fig. S-6. In the light microscopy analysis,xMamin and xFemax diameters were determined manually to make thedata from both techniques comparable. A significant differencewas observed in particle length, represented by xFemax diameter,while the deviations in the width, represented by xMamin diameter,were almost negligible. The particle alignment has more influenceon the measurement in 2D dynamic imaging. During the micro-scopy analysis, particles were aligned perpendicular to themeasurement direction, and thus, the particle alignment onlyslightly influenced the particle size. The observation made byIgathinathane et al. [38] that the measured length depends on ori-entation angle in imaging analysis was confirmed in the present

study. It was shown [38], that correction factors can rectify theoverestimation. The microscopy and 2D dynamic imaging resultswith respect to xFemax diameter can be made comparable if theresults from the imaging analysis are multiplied by cos(45�) [39],as shown in Supplementary Fig. S-6. Igathinathane et al. [38] usedthe

ffiffiffiffip

p/2 (� 0.886) correction factor to reduce the width and

length of rectangular and cubic particles in imaging analysis; thefactor is close to the correction factor of cos(45�) � 0.707. In 2Ddynamic imaging software, the particle thickness is assumed tobe equal to the width. The present microscopy results show thatthe particle thickness of woody and herbaceous feedstocks canbe estimated to be 2/3 of the particle width (xMamin), as shown inSupplementary Fig. S-7. The thickness of larger (>0.6 mm) wheatstraw and pulverized wood particles can be estimated as 1/2 ofthe particle’s width, confirming the results of Momeni [40].

3.3. Representation of biomass particle shape in modeling

In suspension firing, biomass particles undergo rapid heating,drying and devolatization with the formation of char and volatiles.Devolatilization models often assume non-isothermal biomassparticles, and include external and internal heat transfer [17]. Anon-isothermal model has been developed to estimate the yieldsof volatiles and char at different heating rates, high temperatures(up to 1500�C) and is valid for different biomass particle sizes.The particle model was validated against data from separatepyrolysis experiments performed at an intermediate heating rate(10–103 K s�1) in the wire mesh reactor (WMR) and at a high heat-ing rate of (104 K s�1) in the drop tube reactor (DTF) [41]. A woodparticle enters a hot gas stream and is heated up by convection andradiation. The unsteady heat conduction equation (Fourier’s Law)in cylindrical coordinates (f = 1) is used:

cp;s � dTp

dt¼ 1qs

� 1r f

� @@r

r f keff@Tp

@r

� �ð14Þ

The parameters in equation 14 are defined in nomenclature. Theeffective thermal conductivity (keff ) inside the particle is approxi-mated by Bellais and Grønli [42,43]. A biomass particle can be rep-resented as a plate, a cylinder, and a sphere in planar (f = 0),cylindrical (f = 1), and spherical (f = 2) coordinates under theassumption of similar volume to surface ratios using a differentcharacteristic length:

dp ¼ xMamin ðcylinderÞ ð15Þ

dp ¼ 12� xMamin ðplateÞ ð16Þ

dp ¼ 32� xMamin ðsphereÞ ð17Þ

As it has been shown in this work, biomass particles possesslarge aspect ratios so that a spherical representation should beavoided. A cylindrical shape allows treatment of biomass particlesas one-dimensional [9]. Thus, it is recommended to represent bio-mass particles as infinite cylinders, corresponding to f = 1 with aparticle size equal to xMamin diameter, as shown in equation 15.Fig. 7 illustrates the mass loss of 0.2 and 1 mm pulverized woodparticles. The previous results from the 1D model emphasized akey role of intra-particle heat conduction in biomass particle >

0.25mm [41]. Devolatilization time decreased with the higherheating rate in the drop tube reactor compared to the wire meshreactor. The representation of the 0.2 mm particles using differentcharacteristics lengths does not give large deviations with respectto char yield and devolatilization time among the three particlegeometries, as shown in Fig. 7a. The influence of particle shapebecomes more important with the increasing particle size due tothe larger internal temperature gradients, as shown in Fig. 7b.

Fig. 7. Mass loss histories of pulverized wood particles (0.2 and 1 mm) with thesimilar volume to surface ratio and different characteristic lengths which werecalculated in plate-like (n = 0), cylindrical (n = 1) and spherical (n = 2) geometries atthe final temperature of 1400�C during pyrolysis in the wire mesh and drop tubereactors.

682 A. Trubetskaya et al. / Fuel 206 (2017) 675–683

The relative influence of heating rate on devolatilization time of1 mm pulverized wood was less as compared to that for smallerparticles. This is because of the predominance of internal heattransfer control within the large particles.

4. Discussion

Prior to combustion modeling, biomass samples are usuallyanalyzed to obtain the shape parameters (i.e. sphericity, symmetryand aspect ratio) by using one of the discussed techniques. Variousbiomass shapes result in different volume-to-surface area ratioswhich determine heat and mass transfer [44,9]. A spherical parti-cle, as commonly used in literature [45], has a higher volume tosurface area ratio than a cylindrical particle of the same volume.Therefore, particles with a smaller aspect ratio heat up faster,which results in a faster conversion rate. The experimental investi-gations showed significantly smaller aspect ratios of biomassparticles compared to coal, indicating that the spherical represen-tation of a biomass particle (larger volume-to-surface area ratios)overestimates devolatilization time. Lu et al. [46,9] measured andcalculated particle surface area and volume using a three-dimensional particle shape reconstruction algorithm based onthree images taken from orthogonal directions. The particle surface

and volume calculation involved image acquisition and processing,image contour alignment and surface generation. In the presentstudy, particle size distributions obtained by 2D dynamic imagingwere used to calculate the volume to surface ratio, where xMamin

diameter was used as the particle width. The xMamin diameter canbe replaced by xc min when a 2D dynamic imaging device is notavailable, since only small differences occur while representingparticle size distributions, based on volume, over xMamin and xc min

diameters. Alternatively, the average specific surface area can bemeasured by 2D dynamic imaging, and multiplied by the cos(45�) factor. In particle technology, a particle is often representedas an ellipsoid, based on favorable properties such as geometricinterlocking and an accurate description of convex particle shapes[47]. In addition, an ellipsoid resembles a large array of shapes,including that of a flake like particle (oblate ellipsoid) and a rod-like particle (prolate ellipsoid) [11]. In the mathematical combus-tion model, a complete char burnout is a common assumption,so that a rectangular shape can be chosen as the best particle shapedescriptor since the rectangular-shaped particles demonstrate thelongest burnout times. However, the ellipsoidal and rectangularrepresentations are very difficult to model. The cylindrical repre-sentation may give a precise description of char burnout, althoughthe particle volume, compared to the ellipsoidal volume, withequal dimensions tends to be overestimated by the minimal timerequired for the mass and heat transfer calculations. Moreover,the cylindrical representation does not consider the biomass parti-cles’ edges, which influence the heat and mass transfer calculationin combustion modeling.

5. Conclusion

An experimental studywas carried out to investigate the particlesize and shape characteristics of woody and herbaceous biomass.The particle size results obtained by 2D dynamic imaging were inagreement with the sieving data. A significant disparity wasobserved in the laser diffraction and the focused beam reflectancemeasurements. 2D dynamic imaging was found to be the most con-venient characterization method, providing additional informationon particle shape and external surface area. Light microscopy and2D dynamic imaging showed that pulverized wood formedsquare-shaped particles, while the poplar andwheat straw particleswere elongated and of rectangular-shape. It is recommended to rep-resent biomass particles in combustionmodels as infinite cylinders,where the particle width is represented either by xMamin or xc min

diameters. The relative influence of heating rate on devolatilizationtime of larger wood particles was less as compared to that for smal-ler particles, whereas the influence of particle shape became moreimportantwith the increasing particle size due to the predominanceof internal heat transfer control within the large particles.

Acknowledgements

The authors would like to acknowledge the financial supportreceived from the Danish Strategic Research Council (Grant Nr.DSF-10-093956), Kempestiftelse, DONG Energy, Vattenfall andHOFOR. We would like also to thank Ian Haley and Brian O’Sullivanfrom Mettler Toledo for assisting with FBRM measurements. Theauthors thank DTU Combustion and Harmful Emission Controlgroup for the fruitful discussions. Erika Christ is acknowledgedfor the article proof reading.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.fuel.2017.06.052.

A. Trubetskaya et al. / Fuel 206 (2017) 675–683 683

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